Question

According to a study done by a university​ student, the probability a randomly selected individual will not cover his or her mouth when sneezing is

0.267

Suppose you sit on a bench in a mall and observe​ people's habits as they sneeze.

​(​a)

What is the probability that among

18

randomly observed individuals exactly

4

do not cover their mouth when​ sneezing?

​(​b)

What is the probability that among

18

randomly observed individuals fewer than

6

do not cover their mouth when​ sneezing?

​(​c)

Would you be surprised​ if, after observing 18

​individuals, fewer than half covered their mouth when​ sneezing? Why?

Answer 1

Solution:

Given:

p = the probability a randomly selected individual will not cover his or her mouth when sneezing = 0.267

n = 18

a)

We have to find P(X= 4)= ....?

Using Binomial probability formula,

Therefore,

P(X=4)

=0.201

Hence, the probability that among 18 randomly observed individuals exactly 4 do not cover their mouth when​ sneezing = 0.201

b)

We have to find P(X<6) = ...?

That means, P(X<6) = P(X5)

P(X5)= P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)

=0.0037+0.0245+0.0757+0.1472+0.201+0.205

=0.6571

Hence, the probability that among 18 randomly observed individuals fewer than 6 do not cover their mouth when​ sneezing = 0.6571

c)

We have to find P(X<9)=...?

That means, P(X<9) = P(X8)

P(X8)= P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)+P(X=7)+P(X=8)

=0.0037+0.0245+0.0757+0.1472+0.201+0.205+0.1618+0.101+0.0506

=0.9706

Hence, the probability after observing 18 ​individuals, fewer than half covered their mouth when​ sneezing = 0.9706

This probability is high, so I would not surprised.

Done